How do you write # f(x)= x^2 + 6x + 12# in vertex form?
The equation of a parabola in
#"where " (h,k)" are the coordinates of the vertex"#and a is a constant.
#"Rearrange " f(x)=x^2+6x+12" into this form"#
#"using the method of "color(blue)" completing the square"#
#color(white)(f(x))=(x+3)^2+3larrcolor(red)" in vertex form"#
The general vertex form is
with vertex at
Extracting the "spread" factor
Completing the square
Re-writing with a squared binomial and some simplification:
...or in explicit vertex form:
(note that I dropped the
In order to check that I didn't make any mechanical errors, I've plotted the original equation, and it does appear to have the vertex indicated by the derived equation: